33 lines
1.3 KiB
Text
33 lines
1.3 KiB
Text
-- Copyright (c) 2014 Floris van Doorn. All rights reserved.
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-- Released under Apache 2.0 license as described in the file LICENSE.
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-- Author: Floris van Doorn
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import .basic .constructions
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open eq eq.ops category functor natural_transformation category.ops prod category.product
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namespace adjoint
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--representable functor
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definition foo {obC : Type} (C : category obC) : C ×c C ⇒ C ×c C := functor.id
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definition Hom {obC : Type} (C : category obC) : Cᵒᵖ ×c C ⇒ type :=
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@functor.mk _ _ _ _ (λ a, hom (pr1 a) (pr2 a))
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(λ a b f h, pr2 f ∘ h ∘ pr1 f)
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(λ a, funext (λh, !id_left ⬝ !id_right))
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(λ a b c g f, funext (λh,
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show (pr2 g ∘ pr2 f) ∘ h ∘ (pr1 f ∘ pr1 g) = pr2 g ∘ (pr2 f ∘ h ∘ pr1 f) ∘ pr1 g, from sorry))
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--I'm lazy, waiting for automation to fill this
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variables {obC obD : Type} (C : category obC) {D : category obD}
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variables (f : Cᵒᵖ ×c C ⇒ C ×c C) (g : C ×c C ⇒ C ×c C)
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check g ∘f f
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check natural_transformation (Hom D)
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definition adjoint (F : C ⇒ D) (G : D ⇒ C) :=
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natural_transformation (@functor.compose _ _ _ _ _ _ (Hom D) sorry)
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--(Hom C ∘f sorry)
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--product.prod_functor (opposite.opposite_functor F) (functor.ID D)
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end adjoint
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